Internal problem ID [1929]
Book: Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section: Exercis 2, page 5
Problem number: 3(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 12
dsolve(diff(y(x),x)=y(x)*x,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 22
DSolve[y'[x]==y[x]*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to 0 \\ \end{align*}